Self-Adjointness criterion for operators in Fock spaces

Abstract

In this paper we provide a criterion of essential self-adjointness for operators in the tensor product of a separable Hilbert space and a Fock space. The class of operators we consider may contain a self-adjoint part, a part that preserves the number of Fock space particles and a non-diagonal part that is at most quadratic with respect to the creation and annihilation operators. The hypotheses of the criterion are satisfied in several interesting applications.

arXiv comment20 pages

References in corpus (3)

• On the self-adjointness and domain of Pauli-Fierz type Hamiltonians
• Wigner measures approach to the classical limit of the Nelson model: Convergence of dynamics and ground state energy
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• Pauli-Fierz type operators with singular electromagnetic potentials on general domains
• Self-adjointness of a class of multi-spin-boson models with ultraviolet divergences
• Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model
• Microscopic Derivation of Time-dependent Point Interactions
• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model
• Renormalization of spin$\unicode{x2013}$boson interactions mediated by singular form factors
• Self-adjointness and domain of generalized spin-boson models with mild ultraviolet divergences